This theorem is known as max flow-min cut theorem (see [1]} and references therein), that is, the maximal flux of bit threads (over all possible bit thread configurations) connecting a boundary subregion \(A\)  of a Riemannian manifold with its complement \({{A_{\rm {c}}}}\)  is equal to the area of the bulk minimal surface \(\gamma \left( A \right)\)  homologous to \(A\) . Therefore, the famous RT formula which relates the entanglement entropy of a boundary subregion \(A\)  and the area of the bulk minimal extremal surface \({\gamma \left( A \right)}\)  homologous to A [2]}, [3]}, [4]}:
\(S\left( A \right) = \frac{{Area\left( {\gamma \left( A \right)} \right)}}{{4{G_N}}},\) 
